Water-saturated Glass Beads Research Articles

Pore size distribution measurement with magnetic resonance [formula omitted] distributions outside the fast diffusion regime

Based on Brownstein-Tarr (BT) theory, a new method is proposed to determine the pore size distribution which is an important petrophysical property in studying fluid storage and fluid transport in reservoir rocks. For reservoir rocks with large pores, or high surface relaxivity, direct conversion from the magnetic resonance (MR) T2 distribution with the fast diffusion assumption may be unreliable. In this study, the ground mode lifetime T20 distribution was proposed to be utilized to estimate the pore size distribution. The T20 lifetime of large pores within a porous system can be determined directly through experiment. However, the T20 lifetimes of smaller pores may overlap with the first nonground mode T21 lifetimes of the larger pores, which collectively contribute to the MR signal with a shorter lifetime. To accurately determine the T20 lifetime of smaller pores, it is essential to remove the contribution to the distribution of the T21 lifetimes of the larger pores. The T21 distribution can be both experimentally observed and calculated through the proposed method. The proposed pore size distribution method is verified by calculation in the present work. Water-saturated glass bead packs were employed for initial experiments. The calculated pore size, and its distribution, match the geometric pore size. The proposed method was applied to determine the pore size distribution of a Berea sandstone. The results are in good agreement with SEM measurements.

An illustration of the effect of neglecting poroelastic physics of water-saturated glass beads in a laboratory phase speed inference process.

The sound speed of sand has been shown to vary with frequency, yet in many instances in geoacoustic inversions, sand is modeled as a frequency-independent effective fluid. This paper investigates the effect to which assuming a frequency-independent fluid model that neglects poroelasticity can skew parameter estimation in a laboratory layered waveguide consisting of 1-mm diameter water-saturated glass beads (WSGBs), suspended in a water-filled glass tube. The phase speed in the waveguide was measured from 1 to 7 kHz and compared with phase speeds predicted in a finite element simulation of the experiment, where the WSGBs were treated as either a fluid with constant bulk density and frequency-independent or frequency-dependent sound speed, or by an effective density fluid model (EDFM) that includes poroelasticity. Measurement-simulation agreement occurred when using the EDFM to model the WSGB, although neglecting poroelasticity in the simulation only led to a maximum phase speed discrepancy of 8 m/s. However, this effect was significant when an inference process was used to determine the effective fluid properties of the WSGBs. Finally, high-frequency (150 to 450 kHz) direct sound speed measurements of the WSGB were obtained, and best matched the mid-frequency inference results obtained using the EDFM.

Measurements of nonlinearity parameter B/A of water-saturated glass beads under uniaxial compressive loading.

This Letter reports measurements of nonlinearity parameter B/A of water-saturated glass beads under uniaxial compression representative of the gravitational loading in seabed. The finite-amplitude method in conjunction with the multi-Gaussian beam model is used to determine B/A, in which the use of an accurate source function is found to be important in achieving the overall measurement accuracy. The estimated B/A is on the order of a hundred and decreases with increasing uniaxial compression up to 50 kPa, so that B/A could change as much as 20% over a depth of 5 m for a typical coarse sandy sediment.

The effect of pH and ionic strength on the transport of alumina nanofluids in water-saturated porous media

Alumina nanofluids are one of the most useful nanofluids, especially for increasing the thermal conductivity. Due to importance of porous media in the improvement of heat transfer, this study investigates the transport and retention of gamma alumina/water nanofluid in the water-saturated porous media. For this purpose, alumina nanofluids were introduced to the porous media consisting of water-saturated glass beads possessing various pH values (4, 7 and 10) and different ionic strengths (0.001 M of KCl, CaCl2, AlCl3, K2SO4, CaSO4, Al2(SO4)3, K2CO3 and CaCO3). Then the break through curve of each experiment was drawn and modeled by combining classical filtration theory with advection–dispersion equation. Single collector efficiency (η0) and attachment efficiency (α) were calculated by classical filtration theory. Also curve fitting of experiments and modeling was achieved by minimizing the sum of squared residuals, to calculate retardation factor (R) and hydrodynamic dispersion coefficient (D) of each experiment. According to the results, in general, increase in pH and ionic strength will enhance the removal rate coefficient, retardation factor and retention while decreasing the steady-state break through concentration and the hydrodynamic dispersion coefficient. The opposite of this rule was observed and analyzed for aluminum salts. The lowest retention of nanoparticles at 31.04% can be related to their transport in background solution with pH = 4 [α = $$3.87 \times 10^{ - 2}$$ , Katt = $$3.33 \times 10^{ - 3}$$ (min−1), R = 3.93, D = 0.91 (cm2 min−1)], and the highest retention in nanoparticle content of 94.29% was observed in background solution containing CaCO3 [α = $$14.33 \times 10^{ - 2}$$ , Katt = $$137.82 \times 10^{ - 3}$$ (min−1), R = 12.02, D = 0.62 (cm2 min−1)]. Therefore, chemistry of water plays an important role in transport and retention parameters. The classical filtration theory and the advection–dispersion model are able to perfectly model and quantify the parameters of the alumina nanofluid transport in saturated porous media.

Prediction of tortuosity, permeability, and pore radius of water-saturated unconsolidated glass beads and sands.

Tortuosity, permeability, and pore radius, which are parameters in the Biot model, are important for analyzing the elastic wave propagation in water-saturated unconsolidated marine sands. In this study, the formation factor and permeability are measured for 34 kinds of water-saturated glass beads and sands with uniformly sized grains and 73 kinds of water-saturated sands with distributed sized grains. Using these measured data, the empirical equations for the formation factor, cementation exponent, and tortuosity are obtained. The pore shape factor, k0, in the Kozeny-Carman model and pore shape factor, a, in the Revil-Cathles (RC) model are derived. The Hazen, Kozeny-Carman, and RC models are compared for the measured permeability results. Furthermore, the relationship between the tortuosity and permeability is shown. Finally, the ratio of the effective pore radius to effective mean grain diameter is derived.

Heat conduction in two and three-phase media with solid spherical particles of the same diameter

Heat conduction in two and three-phase media, composed of solid spherical particles of the same diameter, is investigated theoretically and experimentally. The theoretical model has no empirical constants and is based on the solution of the Fourier heat conduction equation, under the thermal assumption of parallel heat fluxes, in porous medium with porosity greater than 0.4764. The medium can be two-phase, fully saturated with water or air, or three-phase, partially saturated with water and air. The problem is investigated experimentally with the thermal probe, a vertical cylinder inserted into the glass beads of the diameter of 3 mm. The thermal probe, made in laboratory, has a diameter of 1.5 mm and length 150 mm, and contains an electric heater and a temperature sensor. The perfect line source theory in the transient regime is employed to measure the thermal conductivity of the water saturated glass beads. The theoretical results for the two-phase media, glass beads and water, are in good agreement with the experiments. The results of the theoretical model for the three-phase media, glass beads with water and air, are in good agreement with the experimental data of the literature, and are compared to several theoretical models of the literature.

High frequency p-wave attenuation dispersion in water-saturated granular medium with bimodal grain size distribution

Compressional wave attenuation in water-saturated granular medium depends on both the frequency and grain size. In recent series of high frequency measurements on porous medium, such as water-saturated glass beads and marine sediments, the effect of grain size distribution on attenuation has been investigated, and a variety of grain size dependence on attenuation has been reported. Particularly, dispersion relation in the granular medium with bimodal grain size distribution is significantly different from that in the medium with unimodal grain size distribution. In this study, two sets of glass beads experiments employing unimodal and bimodal grain size distributions are performed. In order to examine wave propagation phenomenon in the bimodal grains, the attenuation dispersion is represented as a function of three parameters; porosity, volume fraction of scatterers, and Rayleigh parameter kd. Heuristic dispersion model considering scattering phenomenon will also be discussed for comparison with measurements.

Modified resonator method for laboratory measurement of the low frequency compressional wave speed in granular sediments

Several models have been developed to describe dispersion in granular sediments. There is an abundance of measurements confirming these models above 10 kHz, obtained via time-of-flight measurements, but there is far less data for accurate model verification under 10 kHz. The present work focuses on laboratory compressional wave speed measurements of water-saturated glass beads in the frequency range 1 kHz to 10 kHz using a resonance tube technique that, in future work, will be scaled in size to attain results below 1 kHz. In previous versions of this technique, the granular sediment completely filled the resonator; however, grain interaction with the resonator walls and the development of grain-to-grain force chains yielded undesirable results. The present method isolates a cylindrical volume of sediment from the resonator wall by a tulle net membrane and a layer of water. The effective sediment wave speed is inferred through the measured system resonance frequencies and a finite-element model that relates the system resonance frequencies to the intrinsic sound speed of the sediment. Sound speed measurements in a model sediment composed of 1-mm-diameter glass beads and distilled water agreed with the Effective Density Fluid Model (EDFM). [Work supported by ONR.]

Influence of natural organic matter on fate and transport of silver nanoparticles in saturated porous media: laboratory experiments and modeling

Understanding the fate and transport of silver nanoparticles (AgNPs) is of importance due to their widespread use and potential harmful effects on humans and the environment. The present study investigates the fate and transport of widely used Creighton AgNPs in saturated porous media. Previous investigations of AgNP transport in the presence of natural organic matter (NOM) report contradictory results regarding how the presence of NOM affected the stability and mobility of AgNPs. In this work, a nonreactive tracer, AgNPs and a mixture of AgNPs and NOM were injected into a background solution (0.01 mM of NaNO3) flowing through laboratory columns packed with water-saturated glass beads to obtain concentration versus time breakthrough curves. Transport of AgNPs in the presence of NOM was simulated with a model that accounted for both reversible and irreversible attachment. Based upon an analysis of the AgNP breakthrough curves, it was found that addition of NOM at concentrations ranging from 1 to 40 mg L−1 resulted in significant decreases in both the zeroth and first moments of the breakthrough curves. These observations may be attributed to NOM promoting AgNP aggregation and irreversible attachment. Raman and surface-enhanced Raman scattering analysis of NOM-AgNP mixtures revealed that a possible interaction of NOM with AgNP occurred through the carboxylic moieties (–COO−) located in the immediate vicinity of the metallic surface. At higher concentrations of NOM, both the zeroth and first moments of the breakthrough curves increased. Based on modeling and the literature, we hypothesize that as the NOM concentration increases, it begins to coat both the AgNPs and the glass beads, leading to a situation where AgNP transport may be described in the same way that transport of a sorbing hydrophobic compound partitioning to an immobile organic phase is typically described, assuming reversible, rate-limited sorption.

Determination of grain size distribution in water-saturated granular medium using p-wave attenuation dispersion

P-wave attenuation in the water-saturated granular medium depends on both the frequency and the grain size. In this study, the use of the attenuation dispersion for the determination of grain size distribution in the water-saturated granular medium is discussed. For the dense granular medium, mathematical model considering multiple scattering is used for regression algorithm by fitting model predictions to the measured attenuation data. Inversion of grain size distribution is carried out numerically, and the results are discussed and compared to measured data for the water-saturated glass beads with unimodal and bimodal distributions.

A General approach to [formula omitted] measurements in the presence of internal gradients

Internal gradients, caused by the magnetic susceptibility difference between the solid surface and imbibed fluids in pores, are a frequently encountered limitation in nuclear magnetic resonance (NMR) analysis of porous materials. The strength of these internal gradients are known to scale with magnetic field strength B0 and their presence prevents quantitative determination of transverse T2 relaxation times, image intensities, and diffusion coefficients. We present a general method for determining “true” T2 relaxation time distributions of liquid saturated porous media in the presence of internal gradients. Our method is demonstrated using water saturated glass bead packs at an intermediate field strength B0=2T, although the technique is applicable to the wide range of porous media found in nature and industry (rocks, soils, cements, catalysts), thereby allowing these materials to be studied at field strengths previously considered to be inappropriate.

Model-Data Comparison of High Frequency Absorption and Velocity for the Water-Saturated Granular Medium

Dispersion relation for the p-wave sound speed and attenuation has been described by several models based on continuum or scattering theory. As an alternative approach, this study proposes a model describing relation for the p-wave in case of elastic grain scatterers existing in background fluid medium. Dispersion relations are shown as a function of different grain size distribution and Rayleigh parameter . For quantitative analysis of the proposed model, experiments are performed using water-saturated glass beads. Two sets of experiments employing unimodal and bimodal grain size distributions are performed and used for comparison with the current proposed model.

High-Frequency Sound-Speed, Attenuation, and Reflection Measurements Using Water-Saturated Glass Beads of Different Sizes

Sound propagation in water-saturated glass beads was studied under controlled laboratory conditions over a frequency range from 200 to 900 kHz for sound-speed measurements and from 200 to 800 kHz for attenuation measurements. The influence of the grain size on both p-wave speed and attenuation was studied using three kinds of glass beads. A strong negative dispersion of the sound speed over the whole frequency range studied was observed with the three different populations of beads used in this experiment (mean grain size: 272 μm, 520 μm, and 1.33 mm). In addition, it was found that not only does the attenuation increase nonlinearly with frequency, but it also depends on the size of the beads. These results are consistent with earlier measurements performed by other researchers over the same frequency range with glass beads of about the same sizes. In this paper, we also discuss the results of the measurement (over a wide frequency range: 200 kHz-1.5 MHz) of the reflection coefficient of a thick slab of glass beads whose surface was smoothed, as well as the correlation between the behavior of this reflection coefficient and the negative dispersion of the sound speed. For this experiment, five populations of beads (91 μm, 272 μm, 520 μm, 133 mm, and 2.98 mm) were used.

Capillary Fracturing in Granular Media

We study the displacement of immiscible fluids in deformable, noncohesive granular media. Experimentally, we inject air into a thin bed of water-saturated glass beads and observe the invasion morphology. The control parameters are the injection rate, the bead size, and the confining stress. We identify three invasion regimes: capillary fingering, viscous fingering, and "capillary fracturing," where capillary forces overcome frictional resistance and induce the opening of conduits. We derive two dimensionless numbers that govern the transition among the different regimes: a modified capillary number and a fracturing number. The experiments and analysis predict the emergence of fracturing in fine-grained media under low confining stress, a phenomenon that likely plays a fundamental role in many natural processes such as primary oil migration, methane venting from lake sediments, and the formation of desiccation cracks.

다공성 입자 매질에서 고주파 영역 음향 측정 자료와 Kramers-Krönig 관계식의 비교

물리현상의 인과성에 대한 필요충분조건은 Kramers-Kr<TEX>$\ddot{o}$</TEX>nig (K-K) 관계식으로 표현된다. 음파에 대한 Kramers-Kr<TEX>$\ddot{o}$</TEX>nig 관계식은 음파의 위상속도 분산식과 감쇠계수 분산식 사이의 힐버트 변환 쌍으로 나타난다. 본 연구에서는 400 kHz-1.1 MHz의 고주파 영역에서 물이 찬 다공성 유리구슬 매질에서 측정된 p파 음속 및 감쇠계수를 Waters 등에 의해 얻어진 미분 형태의 Kramers-Kr<TEX>$\ddot{o}$</TEX>nig 관계식과 정량적으로 비교했다. 감쇠계수는 주파수의 거듭제곱형태를 따르며, 이때 실험값은 Kramers-Kr<TEX>$\ddot{o}$</TEX>nig 관계식과 비교적 정확히 일치한다. The necessary and sufficient condition for causality of a physical system can be expressed as Kramers-Kr<TEX>$\ddot{o}$</TEX>nig (K-K) relation. K-K relation for acoustic wave is a Hilbert transforms pair between dispersion equations of phase speed and attenuation. In this study, we quantitatively compare the acoustic measurements in water-saturated glass beads for the frequency ranges from 400 kHz to 1.1 MHz with the predictions of differential form of K-K relation obtained by Waters et al. For media with attenuation obeying an arbitrary frequency power law, acoustic measurements show good agreements with the predictions of Kramers-Kr<TEX>$\ddot{o}$</TEX>nig relation.

High frequency dispersion model for the water-saturated granular medium

Dispersion relation for the p-wave sound speed and attenuation has been described by several models based on continuum or scattering theory. As an alternative approach, this study proposes a model describing the dispersion relation for the p-wave in case of grain scatterers existing in background porous medium. Dispersion relations are shown as a function of different grain size distribution and Rayleigh parameter ka. For quantitative analysis of the proposed model, experiments are performed using water-saturated glass beads. Two sets of experiments employing unimodal and bimodal grain size distributions are performed and are used for comparison with the current proposed model.

Velocity dispersion and attenuation in granular marine sediments: Comparison of measurements with predictions using acoustic models

The large velocity dispersion recently reported could be explained by a gap stiffness model incorporated into the Biot model (the BIMGS model) proposed by the author. However, at high frequencies, some measured results have been reported for negative velocity dispersion and attenuation proportional to the first to fourth power of frequency. In this study, first, it is shown that the results of velocity dispersion and attenuation calculated using the BIMGS model are consistent with the results measured in two kinds of water-saturated sands with different grain sizes, except in the high-frequency range. Then, the velocity dispersion and attenuation in six kinds of water-saturated glass beads and four kinds of water-saturated silica sands with different grain sizes are measured in the frequency ranges of 80-140 and 300-700 kHz. The measured results are compared with those calculated using the BIMGS model plus some acoustic models. It is shown that the velocity dispersion and attenuation are well predicted by using the BIMGS model in the range of kd ≤ 0.5 (k: wavenumber in water, d: grain diameter) and by using the BIMGS model plus multiple scattering effects in the range of kd ≥ 0.5 in which negative velocity dispersion appears.

Sound speed in water-saturated glass beads as a function of frequency and porosity

Sound propagation in water-saturated granular sediments is known to depend on the sediment porosity, but few data in the literature address both the frequency and porosity dependency. To begin to address this deficiency, a fluidized bed technique was used to control the porosity of an artificial sediment composed of glass spheres of 265 μm diameter. Time-of-flight measurements and the Fourier phase technique were utilized to determine the sound speed for frequencies from 300 to 800 kHz and porosities from 0.37 to 0.43. A Biot-based model qualitatively describes the porosity dependence.

Dynamic acoustoelastic testing of weakly pre-loaded unconsolidated water-saturated glass beads

Dynamic acoustoelastic testing is applied to weakly pre-loaded unconsolidated water-saturated glass beads. The gravitational acceleration produces, on the probed beads, a static stress of order 130 Pa, thus the granular medium is close to the jamming transition. A low-frequency (LF) acoustic wave gently disturbs the medium, inducing successively slight expansion and compaction of the granular packing expected to modulate the number of contacts between beads. Ultrasound (US) pulses are emitted simultaneously to dynamically detect the induced modification of the granular skeleton. US propagation velocity and attenuation both increase when the LF pressure increases. The quadratic nonlinear elastic parameter β, related to the pressure dependence of US propagation velocity, was measured in the range 60-530 if water-saturated glass beads are considered as an effective medium. A dynamic modification of US scattering induced by beads is proposed to modulate US attenuation. Complex hysteretic behaviors and tension-compression asymmetry are also observed and analyzed by time-domain and spectral analyses. Furthermore acoustic nonlinearities are measured in cases of quasi-static and dynamic variations of the LF wave amplitude, providing quantitatively similar acoustic nonlinearities but qualitatively different.

Effect of Particle Shape on Colloid Retention and Release in Saturated Porous Media

Colloidal particles of environmental concern often have nonspherical shapes. However, theories and models such as the classical filtration theory have been developed based on the behavior of spherical particles. This study examined the effect of particle shape on colloid retention (e.g., attachment and straining) and release in saturated porous media. Two- and three-step transport experiments were conducted in water-saturated glass bead columns using colloids dispersed in deionized water and an electrolyte solution. The particles used in the experiments were carboxylate-modified latex colloids of spherical (500 nm diam.) and rod (aspect ratio, 7.0) shapes. The rod-like particles were prepared by stretching the spherical particles. Analysis of the colloid breakthrough curves indicates that particle shape affected transport behavior, but retention did not increase with increasing aspect ratio. Retention of the spherical particles occurred mainly in the secondary energy minimum, whereas retention of rod-like particles occurred in primary and secondary energy minima. There was less straining of rod-like particles compared with spherical ones, indicating that the minor axis was the critical dimension controlling the process. Release of spherical particles on elution was instantaneous, whereas release of rod-like particles was rate limited, giving rise to long tails, implying an orientation effect for rod-like colloids. The results suggest that the differences in electrostatic properties and shape contributed to the observed different retention and release behaviors of the two colloids.